Leads to
Leads to
And, as is well known:
So we have:
So subbing in from this and the the initial condition
With a little rearranging:
Letting z = xy
Since we are looking for integral solutions, let's try the rational root theorem. After sorting the list a bit to get all factors of 56 we find that z = -2 is the only rational solution. (The other two are irrational.) Now there is a detail we need to (quickly) look at. There is no a priori restriction here that says z must be an integer, only x and y. However if we look at the other two solutions for the z equation we can easily see that z = -2 is the only way to go.
So
gives
Thus
Which leads to
This has two solutions: (x,y) = (-2. 1), (1, -2).